The future of electronic warfare, radar, wireless communication, and other advanced electronic systems is trending towards high-frequency band, large bandwidth, wide dynamic range, and integrated multifunctionality. As the operational frequency bands expand and instantaneous bandwidths increase, the instantaneous reception of ultra-wideband radio-frequency (RF) signals has become a challenge. Microwave photonics-based channelized receiving technology, with advantages of large bandwidth, parallel processing capability, and electromagnetic interference resistance, is an enabling technology for the instantaneous reception of ultra-wideband RF signals. This article provides a systematic review of the latest research progress in microwave photonics channelized receiving technology. First, it summarizes and analyzes the working principles and technical characteristics of various microwave photonics channelized receiving techniques. Then, it discusses the image reject technology and self-interference cancellation techniques in the superheterodyne architecture of channelized receivers. Finally, it looks forward to the future development trends of microwave photonics channelized receivers.